We apply the Galerkin FE method to the computational domain in DOT [1]}, the first step of which is to approximate a continuous function by a piecewise-polynomial function. Using the FE representation, let us first discretize an unstructured 2D domain \(\Omega \)  by \(M\)  triangles jointed at \(N\)  vertex nodes (e.g. Fig. REF  left). \(V = \left\lbrace  {{V_k}} \right\rbrace _{k = 1}^N\)  denotes a finite number of \(N\)  nodes. Let \(\vartheta _h\)  be the 2D vector space of continuous piecewise-linear functions on the triangles in the FE mesh. The continuous and piecewise-linear function \(U(x, y): \Omega \rightarrow \mathbb {R}\) , approximating the optical properties on \(\Omega \) , can be written in the form of
\( {U} = \sum \limits _{i = 1}^N {{\mu _i}} {\varphi _i}.\) 
